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new books in algebra number theory related topics lectures on lie groups 2nd edition essential textbooks in mathematics introduction to number theory by wu-yi hsiang uc berkeley hong kong university of science and technology by richard michael hill university college london uk this book is a concise introduction as well as a comprehensive â€œtour of revisitingâ€ the remarkable achievements of s lie w killing,Â Ã‰ cartan and h weyl we begin with the compact theory which is much simpler than that of the general semi-simple lie theory it is a wonderful reality of the lie theory that the clear-cut orbital geometry of the adjoint action of compact lie groups on themselves is not only the key to understand the compact theory but it actually already constitutes the central core of the entire semi-simple theory as well as that of the symmetric spaces this is the main reason that makes the succeeding generalizations to the semi-simple lie theory and then further to the cartan

new books in algebra number theory related topics number theory and its applications ii by hailong li weinan normal university china fuhuo li sanmenxia suda transportation energy saving technology co ltd china nianliang wang shangluo university china shigeru kanemitsu kyushu institute of technology japan this book aims to give a smooth analytic continuation from basic subjects including linear algebra group theory hilbert space theory etc to number theory by way of plenty of practical examples and worked-out exercises the scope is from these basic subjects made applicable to number-theoretic settings to advanced number theory then the book can be read without tears and it will be of immense help to the reader to acquire basic sound skills of number theory and its applications readership advanced undergraduate students graduate students and researchers interested in the use of operators through number-theoretic examples number-theoretic control systems applications of number

new books in algebra number theory related topics compactifications of pel-type shimura varieties and kuga families with ordinary loci by kai-wen lan university of minnesota twin cities usa this book is a comprehensive treatise on the partial toroidal and minimal compactifications of the ordinary loci of pel-type shimura varieties and kuga families and on the canonical and subcanonical extensions of automorphic bundles the results in this book serve as the logical foundation of several recent developments in the theory of p-adic automorphic forms and of the authorâ€™s work with harris taylor and thorne on the construction of galois representations without any polarizability conditions which is a major breakthrough in the langlands program this book is important for active researchers and graduate students who need to understand the above-mentioned recent works and is written with such users of the theory in mind providing plenty of explanations and background materials which

new books in algebra number theory related topics the book of numbers describes natural numbers in terms of their nature laws history and current status 368pp 978-981-4759-43-4 us$58 Â£48 abstract algebra 2nd edition introduction to groups rings and fields with applications contains applications to demonstrate the power of the abstract ideas introduced 576pp 978-981-4730-54-9pbk us$68 Â£56 a first course in linear algebra contemporary developments in finite fields and applications include cryptography coding theory structure of finite fields algorithms curves over finite fields and further applications 372pp 978-981-4719-25-4 us$118 Â£98 elementary introduction to applied matrix theory and its new results obtained in recent years Â£40 uses straightforward and simple english and is especially useful for students who are not native speakers of english exercises in linear algebra 388pp 978-981-3143-11-1pbk us$48 Â£40 232pp 978-981-3143-04-3pbk us$38 Â£32 automated